Question

Solve for all possible values of the real numbers $\mathit{x}$ and $\mathit{y}$ in the following equations.

$\mathit{x}\mathbf{+}\mathit{i}\mathit{y}\mathbf{=}\mathbf{3}\mathit{i}\mathbf{-}\mathbf{4}$

Short answer

The answer is obtained as: $x=-4,y=3$.

Step-by-step solution

Given information

It is given that $x+iy=3i-4$.

Definition of a complex number

Every complex number can be written as:

$z=a+bi$

Where andare both real numbers, z is the complex number, and i is known as iota, which makes z a complex number.

Begin by stating the given information

State the given information as:

$x=iy=3i-4$

Equate like terms

Equate like terms from both sides as:

$$\begin{gathered} x=-4 \\ \mathrm{and} \\ y=3 \end{gathered}$$

Thus, the final answer is obtained:

$x=-4,y=3$